# Frequency Error-Guided Under-sampling Optimization for Multi-Contrast MRI Reconstruction

arXiv: https://arxiv.org/abs/2601.09316 · HTML: https://mlsanity.com/paper/2601.09316/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 48 references that are in the map.
- First posted on arXiv 14 Jan 2026.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Deep Convolutional Neural Network for Multi-modal Image Restoration and Fusion](https://mlsanity.com/paper/1910.04066/) (2019)
- [DuDoRNet: Learning a Dual-Domain Recurrent Network for Fast MRI Reconstruction with Deep T1 Prior](https://mlsanity.com/paper/2001.03799/) (2020)
- [Deep Residual Learning for Accelerated MRI using Magnitude and Phase Networks](https://mlsanity.com/paper/1804.00432/) (2018)
- [Multi-Contrast Super-Resolution MRI Through a Progressive Network](https://mlsanity.com/paper/1908.01612/) (2019)
- [Multi-Modal Transformer for Accelerated MR Imaging](https://mlsanity.com/paper/2106.14248/) (2021)
- [Transformer-empowered Multi-scale Contextual Matching and Aggregation for Multi-contrast MRI Super-resolution](https://mlsanity.com/paper/2203.13963/) (2022)
- [Learning the Sampling Pattern for MRI](https://mlsanity.com/paper/1906.08754/) (2019)
- [Multi-Modal MRI Reconstruction Assisted with Spatial Alignment Network](https://mlsanity.com/paper/2108.05603/) (2021)
- [MMR-Mamba: Multi-Modal MRI Reconstruction with Mamba and Spatial-Frequency Information Fusion](https://mlsanity.com/paper/2406.18950/) (2024)
- [An Inertial Block Majorization Minimization Framework for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2010.12133/) (2020)
- [Complex Fully Convolutional Neural Networks for MR Image Reconstruction](https://mlsanity.com/paper/1807.03343/) (2018)
- [DH-Mamba: Exploring Dual-domain Hierarchical State Space Models for MRI Reconstruction](https://mlsanity.com/paper/2501.08163/) (2025)
- [Deep Unfolding Network with Spatial Alignment for multi-modal MRI reconstruction](https://mlsanity.com/paper/2312.16998/) (2023)

## Abstract (arXiv)

Magnetic resonance imaging (MRI) plays a vital role in clinical diagnostics, yet it remains hindered by long acquisition times and motion artifacts. Multi-contrast MRI reconstruction has emerged as a promising direction by leveraging complementary information from fully-sampled reference scans. However, existing approaches suffer from three major limitations: (1) superficial reference fusion strategies, such as simple concatenation, (2) insufficient utilization of the complementary information provided by the reference contrast, and (3) fixed under-sampling patterns. We propose an efficient and interpretable frequency error-guided reconstruction framework to tackle these issues. We first employ a conditional diffusion model to learn a Frequency Error Prior (FEP), which is then incorporated into a unified framework for jointly optimizing both the under-sampling pattern and the reconstruction network. The proposed reconstruction model employs a model-driven deep unfolding framework that jointly exploits frequency- and image-domain information. In addition, a spatial alignment module and a reference feature decomposition strategy are incorporated to improve reconstruction quality and bridge model-based optimization with data-driven learning for improved physical interpretability. Comprehensive validation across multiple imaging modalities, acceleration rates (4-30x), and sampling schemes demonstrates consistent superiority over state-of-the-art methods in both quantitative metrics and visual quality. All codes are available at https://github.com/fangxinming/JUF-MRI.